place value

Place value is the value of each digit in a number. The value of every digit in a number is different based on its position. A number might have two similar digits but different values, which are decided by the position that the digits hold in the number. Place value is the value of a digit according to its position in the number such as ones, tens, hundreds, and so on. In the below example, number 2153 has four digits 2, 1, 5, and 3. The values of these digits depend on the position of the digit in the number. Place value of 2 is 2 thousands, 1 is 1 hundred, 5 is 5 tens or fifty, and 3 is 3 ones or simply three. 

Place value charts help us to make sure that the digits are aligned in the correct places. To accurately identify the positional values of different digits in a number, we first write the given digits in the place value chart to check their position. The International place value chart is based on the Internationally accepted numeral system. Let us see how number 2153 fits in the below place value chart: 

So you can clearly identify that 2 is in the thousands place, 1 in hundreds, 5 in Tens, and 3 in the ones place. 

The place value system is based on powers of 10, with each position to the left representing a value that is ten times greater than the position to its right. The positions or places in a number are named after the powers of 10, such as ones, tens, hundreds, thousands, etc.

In a number, the rightmost position represents the ones place, followed by the tens place, hundreds place, thousands place, and so on.

Digit	Position	Place Value
3	1	3 × 1 = 3
5	10	5 × 10 = 50
1	100	1 × 100 = 100
2	1000	2 × 1000 = 2000

The place value in numbers can be expressed in two different ways. For example, the place value of 5 in 2153 can be expressed as 5 tens, or 50.

How to write Numbers in Expanded form

Step 1: Get the standard form of the number. For example, 2153.

Step 2: Identify the place value of the given number using the place value chart. The place value chart of 2153 is given above. 

2 - Thousands

1 - Hundred

5 - Tens

3 - Ones

Step 3: Multiply the given digit by its place value and represent the number in the form of (digit × place value).  

2 × 1000, 1 × 100, 5 × 10, 3 × 1

Step 4: Finally, represent all the numbers as the sum of (digit × place value) form, which is the expanded form of the number. 

2153 = 2 × 1000 + 1 × 100 + 5 × 10 + 3 × 1 

or we can write it as, 2153 = 2000 + 100 + 50 + 3 

A number written in expanded form looks like a long addition problem.

Place Value and Face Value

The face value of a digit in any number is the digit itself. Whether the number is single-digit, double-digit, or any number, each digit has its face value. For example:

• If 8 is the number, the face value of 8 is 8, and the place value of 8 is also 8 as 8 × 1 = 8.
• For a given number 84, the face value of 8 is 8 and its place value is 80, as 8 × 10 = 80.
• For number 823, the face value of 8 is 8 and its place value is 800, as 8 × 100 = 800.